Caputo and related fractional derivatives in singular systems

By using the Caputo (C) fractional derivative and two recently defined alternative versions of this derivative, the Caputo-Fabrizio (CF) and the Atangana-Baleanu (AB) fractional derivative, firstly we focus on singular linear systems of fractional differential equations with constant coefficients that can be non-square matrices, or square & singular. We study existence of solutions and provide formulas for the case that there do exist solutions. Then, we study the existence of unique solution for given initial conditions. Several numerical examples are given to justify our theory.